Algorithm 1: Calculates the neighbor distance

Require: y; μi; c

Ensure: Returns the neighbor distance, di(c).

Let i1, …, in be a permutation on 1, …, n such that, if

$u_r=\mathit{max}\left\{{\mu }_{i,i_r}\left(1-y_{i_r}\right),{\mu }_{i,i_r}\left(0-y_{i_r}\right)\right\}$

then u1 ≥ u2 ≥ ⋯ ≥ un.

Let j1, …, jn be a permutation on 1, …, n such that, if

$l_r=\mathit{min}\left\{{\mu }_{i,j_r}\left(1-y_{j_r}\right),{\mu }_{i,j_r}\left(0-y_{j_r}\right)\right\}$

then l1 ≤ l2 ≤ ⋯ ≤ ln.

Let $U_r={\sum }_{j=1}^k$ uj and $L_r={\sum }_{j=1}^k$ lj for k = 1, ⋯, n

Return r such that c − μi · y ∈ [Lr+1, Lr) ∪ (Ur, Ur+1]